This is an old question, but it's a common problem with load balanced sites. There are two settings to be aware of that could be contributing to this issue.
The first is the actual persistence timeout. You can check the persistence setting for a given site on the Big-IP by choosing the appropriate virtual server, then going to the resources tab. Check the value of the Default Persistence Profile. Then look under Local Traffic > Profiles > Persistence to see what timeout this particular profile corresponds to.
The other thing to check is the TCP idle timeout. By default this is 5 minutes, so it's common for it to kill long running database transactions. To find out what this is set to, under the virtual server, check the Protocol Profile. Then go to Local Traffic > Profiles > Protocol > TCP and find Idle Timeout in the profile.